Factor Quadratic Equations

Algebra 1GCSEÅrskurs 9

Problem

Factor: x² + 5x + 6

📝Step-by-Step Solution

Identify what we need

For x² + bx + c, we need two numbers that: multiply to give c (6), AND add to give b (5).

Need: ? × ? = 6 and ? + ? = 5

List factor pairs of 6

Factor pairs of 6: (1, 6), (2, 3), (-1, -6), (-2, -3)

Find the pair that adds to 5

1 + 6 = 7 ✗, 2 + 3 = 5 ✓. The numbers are 2 and 3!

2 × 3 = 6 ✓ and 2 + 3 = 5 ✓

Write as two binomials

x² + 5x + 6 = (x + 2)(x + 3)

Check by expanding

(x + 2)(x + 3) = x² + 3x + 2x + 6 = x² + 5x + 6 ✓

✅Final Answer

(x + 2)(x + 3)

Factoring reverses the FOIL method. The factored form helps us solve equations: if x² + 5x + 6 = 0, then (x + 2)(x + 3) = 0, so x = -2 or x = -3. Remember: when c is positive and b is positive, both factors are positive.

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